Question

eva invested $31,000 in an account paying an interest rate of 3.8% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 20 years?

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $A = Pe^{rt}$, where:

• $P$ = principal amount,
• $r$ = annual interest rate (decimal),
• $t$ = time in years,
• $A$ = final amount.

Step2: Convert rate to decimal

$r = \frac{3.8}{100} = 0.038$

Step3: Substitute values into formula

$P = 31000$, $r=0.038$, $t=20$
$A = 31000 \times e^{0.038 \times 20}$

Step4: Calculate exponent term

$0.038 \times 20 = 0.76$
$A = 31000 \times e^{0.76}$

Step5: Compute final amount

$e^{0.76} \approx 2.1383$
$A \approx 31000 \times 2.1383 = 66287.30$

Answer:

$\$66287.30$